Airbags covers on a viewed side facing the vehicle interior should have a pleasant appearance, but on the other hand should also have a weakening which reliably breaks in the case of activation of the airbag. An attractive surface can be achieved by way of using real leather, but this material is more difficult to process than artificial leather or similar materials for example. Specifically, outlines of the incorporated weakening become apparent, at least under different climatic conditions, such as e.g. are present with a climate change test, on incorporating a weakening into the leather. Solutions which are suggested for this, such as a punching of the leather with a suitable tool, as has been suggested e.g. in DE 100 55 546 A1, however have the disadvantage that the introduced cuts can not only gape under the influence of the temperature, but the leather fibers can also be squashed and compressed, which on the viewed side leads to visibly greasy/shiny regions. With other methods such as perforation for example, a widening of a hole is effected, wherein leather fibers are quasi displaced and do not return into their initial shape. A continuous displacement of the leather fibers and an accordingly deeper cut for incorporating the desired weakening occurs when cutting into the leather, so that here too, the weakening can become visible.